| Copula is a new method to construct a joint distribution with marginal distributions,and it is a powerful tool to structure a multi—dependent random variables for joint distri—bution．Addition,It also reflects the superiority in many aspects:It can solve the difficultof building the joint distributions for Multi—dimensional random variables which Can besplit into independent two questions,the one is to estimate the marginal distributions,the other is to calculate the correlation between two variables；To construct the rankcorrelation coefficient to replace of the linear correlation coefficient,etc．Because Copula function has huge application potential in statistics,many scholarsdevoted to the Copula fundamental research,and they have gotten many great progresses．Therefore the theory of using Copula has tended to be mature,especially many overseasexperts give Copula function with high appraisal in their articles．Fortunately,thereare many authors are absorbed in the Copula research in our country recently,but themajority of articles are concentrating in the financial theory research,there are littlearticles are written about the Copula application in Actuary Mathematics．Therefore 1will introduce some elementary Copula function theories in Actuarial Mathematics in myarticle,and use the data to make some models．The main contents,that is the focuses in my article Can be summarized as follows:1．Firstly,1 will introduce the production,the development and the significanceof Copula function．Then I summarize the results that our predecessors have gotten inCopula function development history,and these conclusions will be described concretelyand systemic in the article．At the same time,locating to the Actuarial Mathematics,showing the forefront issues about Actuarial．2．Beginning with some important theorems and lemmas,1 will introduce the Copulafunction elementary knowledge with some important theorems and the lemmas．Includingthe related definition of Copula,Copula and the uniformity,the dependence measure,survives Copula,as well as the Copula function and the random variable．In order to solve actual problems through specific treatment, we must focus on Archimedes Copula, because it makes the application of Copula become easy, practical. Undoubt Archimedes Copula is the most important function, therefore its domain can not be substituted.3. In my article, there are a variety of models to be fitted and tested the life table. Eventually I find a relatively good model and parameter values. The conclusion between the two models is discovered that the partial optimum values of the Heligman-Pollard model does not better than the model what this article uses: linearity fitting with Several kinds of survival distributed. I believe it is valuable to research the life actuarial theory. On the base of the life curves, using the husbands and wives' data from insurance company, the joint distribution function of husbands and wives' union life condition has been constructed with Copula. Obviously, from the result, the conclusion is surpasses than the tradition conclusion that they are independent.4. Finally, analyzing the actual data about respiratory disorder disease and circulatory disease in Urumqi Centers for Disease Control, simplifying the model, predicting the relationship between the two disease, fitting the joint distribution of respiratory disorder disease and circulatory disease. Then I make a very good conclusion: the data what is fitted with Pareto-Copula function is better than the other data which is directly fitted with the polynomial function. At the same time it confirmed that Copula function is important to study Actuarial mathematics. |
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